The 99 equal temperament, often abbreviated 99-tET, 99-EDO, or 99-ET, is the scale derived by dividing the octave into 99 equally-sized steps, where each step represents a frequency ratio of 12.1212 cents. It is a very strong 7-limit (and 9 odd limit) temperament, but extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far of the mark. It tempers out 3136/3125, 5120/5103, 6144/6125, 2401/2400 and 4375/4374, and supports hemififths, amity, parakleismic, hemiwürschmidt and ennealimmal temperaments, and is pretty well a perfect tuning for hendecatonic temperament. It has a sound defined by the slight sharpness (1.075, 1.565, 0.871 cents) of its 3, 5, and 7.
Using the patent val, <99 157 230 278 342|, 99 is the optimal patent val for the rank four temperament tempering out 121/120; zeus, the rank three temperament tempering out 121/120 and 176/175; hemiwur, one of the rank two 11-limit extensions of hemiwürschmidt; and hitchcock (11-limit amity), the rank two temperament which also tempers out 2200/2187. Using the <99 157 230 278 343| ("99e") val, 99 tempers out 896/891, 243/242, 441/440 and 540/539, and is an excellent tuning for the 11-limit version of hemififths temperament. Hence 99, in spite of the fact that it tunes 11 relatively badly, is an important 11-limit tuning in more than one way.
Using the patent val, <99 157 230 278 342|, 99 is the optimal patent val for the rank four temperament tempering out 121/120; zeus, the rank three temperament tempering out 121/120 and 176/175; hemiwur, one of the rank two 11-limit extensions of hemiwürschmidt; and hitchcock (11-limit amity), the rank two temperament which also tempers out 2200/2187. Using the <99 157 230 278 343| ("99e") val, 99 tempers out 896/891, 243/242, 441/440 and 540/539, and is an excellent tuning for the 11-limit version of hemififths temperament. Hence 99, in spite of the fact that it tunes 11 relatively badly, is an important 11-limit tuning in more than one way.
Scales
tutone6tutone7
tutone13
zeus7tri
zeus8tri
Music in 99edo
Nonaginta et Novem play by Gene Ward SmithBenny Smith-Palestrina in zeus7tri
Intervals